Calculation of reliability function and remaining useful life for a Markov failure time process
Bibliographic record
Abstract
Reliability analysts are interested in calculating a reliability function (RF), e.g. in order to establish an optimal replacement policy. To implement this policy, it is often important to include measured condition information, such as those from oil or vibration analysis. Information from condition monitoring can be included in reliability analysis by considering the hazard rate function as a function of a stochastic covariate process. In this paper, the failure process along with the covariate process is represented by a discrete Markov process. Methods are designed for calculating the conditional and unconditional RFs and for computing the remaining useful life (RUL) as a function of the current conditions. It is shown that a function that appears in the computation can be obtained as a solution to a Kolmogorov-type system of differential equations. The product-integration method is suggested as the main general method for numerical calculation. The same method is also used to calculate the RUL. Illustration of the main concepts is given using field data from a transmission's oil analysis histories.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".